TY - JFULL
AU - Rui Zhang and Yongqi Sun and and Yali Wu
PY - 2013/2/
TI - The Bipartite Ramsey Numbers b(C2m; C2n)
T2 - International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
SP - 151
EP - 155
EM - yqsun@bjtu.edu.cn
VL - 7
SN - 1307-6892
UR - http://waset.org/publications/15580
PU - World Academy of Science, Engineering and Technology
NX - International Science Index 73, 2013
N2 - Given bipartite graphs H1 and H2, the bipartite Ramsey number b(H1;H2) is the smallest integer b such that any subgraph G of the complete bipartite graph Kb,b, either G contains a copy of H1 or its complement relative to Kb,b contains a copy of H2. It is known that b(K2,2;K2,2) = 5, b(K2,3;K2,3) = 9, b(K2,4;K2,4) = 14 and b(K3,3;K3,3) = 17. In this paper we study the case that both H1 and H2 are even cycles, prove that b(C2m;C2n) ≥ m + n - 1 for m = n, and b(C2m;C6) = m + 2 for m ≥ 4.
ER -